Using Latent Class Models To Study The Performance Of Diagnostic Tests In Diagnosising Schistosomiasis

BackgroundSchistosomiasis ranks second, behind malaria, among human parasitic diseases in terms of public health and socioeconomic importance in tropical and sub-tropical areas. A highly sensitive and specific diagnostic test for schistosomiasis infection is fundermental to the development and assessment of control and elimination program for schistosomiasis.Kato-Katz technique, which is simple to perform and requires a minimum of equipment, is one of the most popular diagnostic tests for schistosomiasis infection. However, a shortcoming of the Kato-Katz technique is that it has a low sensitivity and its accuracy is limited by day-to-day variation in schistosome egg excretion. Another method for the diagnosis of schistosomiasis is the detection of circulating cathodic antigens （CCA） in blood or urine. CCA assays are specific for current infection and can provide some information about infection intensity. Within the last few years, two urine CCA assays were developed and became commercially available. The first used a colloidal carbon conjugate of a monoclonal antibody specific for Schistosoma CCA and was designed for use in the laboratory （CCA₂）. The second was a gold-conjugated, lateral flow cassette-based assay, which was designed to a point of contact test （CCA₁）. CCA assays tend to be more sensitive than Kato-Katz technique. However, neither Kato-Katz nor CCA can accurately distinguish infected population from infection-free ones. Actually, there is no gold standard for the diagnosis of schistosomiasis infection.The assessment of the diagnostic accuracy is quite straightforward when a gold standard test is available. However, an error-free reference test is usually out of reach in real situations. Comparison of the diagnostic test to a method that is not truly a gold standard leads to biased results. Discrepant resolution （DR） and composite reference standards （CRS）, which intend to improve both sensitivity and specificity of the reference test by combining results of several imperfect diagnostic tests, were developed to assess the performance of a new diagnostic test in the absence of a gold standard.A key problem with DR has to do with the ambiguous interpretation of the sensitivity and specificity estimators obtained. The standard, relative to which accuracy is measured, depends intrinsically on the results of the new test. CRS tends to be more expensive as compared to DR. More importantly, neither DR nor CRS could perform as accurately as a true gold standard. Therefore, caution should be taken in useing results estimated by DR and CRS.Recently, some researchers have tried to develop sophisticated statistical models to obtain more reliable empirical estimators of sensitivities and specificities of diagnostic tests, and prevalence of a certain disease. Latent class model, which relates a set of observed discrete multivariate variables to a set of unobservable latent variables, is the most effective method in addressing the uncertainties around the sensitivities and specificities of several imperfect diagnostic tests. In the typical application of the latent class method, one assumes that test results of a set of imperfect diagnostic tests are independent, conditional on the true diagnostic status of the subject.Yet, the typical conditional dependence latent class model leads to several disadvantages. Firstly, since2k equations are available in estimating2k+1parameters, the model is unidentifiable when k≤2（k is the number of diagnostic tests）. Secondly, the typical latent class model fails to take into account the influence of covariances, which may result in biased estimates of parameters. Thirdly, repeat observed results of a certain diagnostic test is required to be transformed into a single categorical variable, which may bring about ambiguous interpretation of the test result.ObjectiveWe assessed and compared sensitivity and specificity of Kato-Katz, CCA₁and CCA₂through newly developed latent class models which depended on mixture binomial distributions. Also, we estimated the infection prevalence of Shistosoma mansoni in Cameroon using these latent class models. Finally, we compared and distinguished the optimal statistical model in our data setting.Data sourceFrom February2011to Match2011, Investigators in Cameroon carried out a cross-sectional survey in Yaounde, Makenene and Njombe. A total of750primary school children were randomly selected. Children who had submitted an informed consent form were invited to provide three fresh morning stool samples and three urine samples in a week. Kato-Katz, CCA₁and CCA₂were used to analyze colleted samples. Variables such as sex, age and city which might have influence on the infection prevalence of Shistosoma mansoni were also collected Latent class modelsA total of6latent class models were created for the assessment of diagnostic performance and for the prediction of schistosomiasis infection. Covariances such as sex, age and city were incorporated into those statistical models except model1. Testing results of Kato-Katz were coded as a dichotomous variable in model1and model2. Zero-inflated Poisson and zero-inflated Negative Binomial models were considered in developing model3, model4, model5and model6in order to account for extra zeros of egg counts.The EM algorithm was used to get the maximum likelihood parameters. Accelerated EM algorithm, which achieves a quadratic rate of convergence by incorporating Newton-Raphson techniques in M step, was utilized in model3, model4, model5and model6. AIC, BIC and hypothesis testing regarding the selection over-dispersed models were employed to distinguish the optimal model.ResultsAmong Kato-Katz, CCA₁and CCA₂, CCA₁had the highest sensitivity （higher than0.86） and lowest specificity （lower than0.74）; Kato-Katz had a perfect specificity which reached1.00, but its sensitivity was much lower than CCA₁.Sensitivity and specificity of a specific diagnostic test estimated from its own testing results tended to be higher than those estimated from combined testing results of three diagnostic tests.Sensitivity of CCA₁estimated by model2, model5and model6was significantly larger than that by model1, model3and model4. Sensitivity and specificity of CCA₂estimated by model3and model4were significantly different from those estimated by model1, model2, model5and model6. Specificity of CCA₂estimated by model3and model4were significantly smaller than those estimated by model1, model2, model5and model6. If only sex and age were included into latent class models, specificity of CCA₁and CCA₂decreased, while sensitivity of CCA₂increased.Estimates of infection prevalence of Schistosoma mansoni obtained from latent class models tended to be larger than posive rates of Kato-Katz, CCA₁and CCA₂directly calculated from their testing results.Over-dispersion parameters in model4and model6were not significantly different from zero, which indicated that Possion model was superior to Negative Binomial model in our data setting. AIC and BIC values were smaller under model4and model5than under model3and model6.Among three investigated cities in Cameroon, infection prevalence of Schistosoma mansoni was highest in Makenene, and was loweset in Yaounde. Within the same city, infection prevalence of Schistosoma mansoni was higher in boys than in girls, and was increased with the increment of age. In model3and model4, infection prevalence was much the same between boys and girls given in the same cities and of the same ages. Infection prevalence estimated by model2, model5and model6was correspondingly larger than that by model3and model4. Besides, infection prevalence of Schistosoma mansoni among boys was significantly larger than that among girls under model2, model5and model6.The smaller the reference sensitivity was, the larger the sensitivity was obtained through DR, CRS and traditional imperfect reference. Estimates of infection prevalence of Schistosoma mansoni were larger under latent class models than those under DR, CRS and traditional imperfect reference. ConclusionsIn the present study, we developed6conditional dependence latent class models based on various hypthesis. These improve statistical models were used to evaluate sensitivity and specificity of Kato-Katz, CCA₁and CCA₂. Our study is of significance to the monitor and assessment of control and elimination program for schistosomiasis. According to study results, CCA₁has the highest sensitivity but lowest specificity; Kato-Katz has a perfect specificity but lower sensitivity.In addition, we assessed the performance of6newly developed latent class models in our study. It seems that zero-inflated Poisson model is superior to zero-inflated Negative Binomial model in estimating the infection probability of Schistosoma mansoni through Kato-Katz technique. Among all6statistical models, model2and model5fit best in our data setting. Since model2has to change testing results of Kato-Katz into a dichotomous variable, it contains less information than model5. Therefore, we recommend model5in our data setting, whose kernel of complete-data likelihood is:Zij denotes the number of positive test results for diagnostic test j out of Nij replicates; αj denotes sthe sensitivity of test j and βj denotes the corresponding specificity of that test; Yik denotes the number of egg counts of subject i in the k-th Kato-Katz test; ui and vik are two latent dichotomous variables; γ s are regression coefficients of the logistic regression component for estimate of prevalence of schistosomiasis infection; ζs are regression coefficients of the log regression component for estimate of intensity of schistosomiasis infection;■s are regression coefficients of the logistic regression component for estimate of the probability of laying eggs given infected by Schistosoma mansoni.